PERTURBATIONS OF VECTOR FIELDS ON TORI: RESONANT NORMAL FORMS AND DIOPHANTINE PHENOMENA

Normal Forms of Vector Fields on Poisson Manifolds

We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.

Polynomial Normal Forms for Vector Fields on R3

The present paper is devoted to studying a class of smoothly (C∞) finitely determined vector fields on R3. Given any such generic local system of the form ẋ = Ax + · · · , where A is a 3 × 3 matrix, we find the minimal possible number i(A) such that the vector field is i(A)-jet determined, and we find the number μ(A) of moduli in the C∞ classification. We also give a list of the simplest normal...

Robust normal forms for saddles of analytic vector fields

The aim of this paper is to introduce a technique for describing trajectories of systems of ordinary differential equations (ODEs) passing near saddle-fixed points. In contrast to classical linearization techniques, the methods of this paper allow for perturbations of the underlying vector fields. This robustness is vital when modelling systems containing small uncertainties, and in the develop...

Normal Forms of Analytic Perturbations of Quasihomogeneous Vector Fields: Rigidity, Invariant Analytic Sets and Exponentially Small Approximation

Unique Normal Forms for Nilpotent Planar Vector Fields